3 x 3 Determinants A Short Cut Method

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3 x 3 DeterminantsA Short Cut Method

• By
• Dr. Julia Arnold

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There are short cut methods of finding the
determinant for the 2x2 matrix and the 3x3
matrix. All square matrices of size 4 and above
must use the Cofactor and Minors method of
finding the determinant. Dr. Burger, in his
notes, has shown you the Cofactor method for the
3x3 determinant and at the beginning of the notes
he shows the short cut method which may appear
confusing. I would like to show you an easier
version of the short cut method for finding
determinants for a 3x3 matrix.
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We will use the same example that is in the notes
Example
From the notes we already know the answer is -14
Here is the easy way to arrive at that answer
Step 1 Copy column 1 and 2 next to the matrix.
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Step 2 Beginning with 2, multiply the numbers
on the diagonal (3 numbers only).
To that add the product of the 3 numbers on the
next diagonal.
And again, the product of the 3 numbers on the
last diagonal.
Now beginning with the 1 in the upper right hand
corner, we are going to come back, multiplying
the numbers on the diagonals. We will also sum
these and then subtract the answer from the sum
above.
Now subtract 0 - 14 - 14